RC & RL transients worksheet with answers

Free printable RC & RL transients worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
+−Vs​9 Vt = 0R = 3.3 kΩC68 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the time constant τ of the circuit.

Vs = 9 VR = 3.3 kΩC = 68 µF
τ = ms
2.Easy
+−Vs​10 Vt = 0R = 2.2 kΩC68 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 75 ms.

Vs = 10 VR = 2.2 kΩC = 68 µFt = 75 ms
vC = V
3.Medium
+−Vs​15 Vt = 0R = 22 ΩL22 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the voltage vL across the inductor at t = 1 ms.

Vs = 15 VR = 22 ΩL = 22 mHt = 1 ms
vL = V
4.Medium
+−Vs​24 Vt = 0R1​ = 1 kΩR2​ = 1 kΩC220 µF+−vC​

The source Vₛ charges the capacitor through R₁, and R₂ is connected in parallel with C. The capacitor is uncharged when the switch closes at t = 0. Find the time constant τ of the circuit after the switch closes.

Vs = 24 VR1 = 1 kΩR2 = 1 kΩC = 220 µF
τ = ms
5.Hard
+−Vs​12 Vt = 0R = 3.3 kΩC22 µF+−vC​vC​(0) = 18 V

Just before the switch closes at t = 0, the capacitor holds 18 V with the polarity shown. Find the capacitor voltage vC at t = 80 ms.

Vs = 12 VR = 3.3 kΩC = 22 µFvC(0) = 18 Vt = 80 ms
vC = V
6.Hard
+−Vs​24 Vt = 0R = 1 kΩC10 µF+−vC​vC​(0) = 4 V

Just before the switch closes at t = 0, the capacitor holds 4 V with the polarity shown. How long does it take for vC to reach 20 V? Find t.

Vs = 24 VR = 1 kΩC = 10 µFvC(0) = 4 V
t = ms

Answer key

  1. 1. τ = 224.4 ms
  2. 2. vC = 3.943 V
  3. 3. vL = 5.518 V
  4. 4. τ = 110 ms
  5. 5. vC = 13.99 V
  6. 6. t = 16.09 ms

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